This paper presents a systematic method for tuning the weighting matrices of a Linear Quadratic Regulator (LQR) applied to Automatic Generation Control (AGC) in a power system where Combined Cycle Gas Turbines (CCGTs) provide the primary regulation service. CCGT units offer fast ramp rates and high efficiency, making them well suited for load following and frequency control. However, the design of the LQR requires careful selection of the state weighting matrix Q and the control weighting scalar R, which directly govern the trade off between frequency regulation quality and control effort. Instead of heuristic or trial and error choices, we formulate a multi objective cost function that minimises the Integral of Time weighted Absolute Error (ITAE), control energy, and frequency nadir. The Nelder Mead simplex algorithm is employed to optimise the diagonal entries of Q and the scalar R for a single area CCGT dominated system. Two case studies with different step load disturbance patterns are simulated in MATLAB. The optimisation consistently drives R to zero, yielding extremely high LQR gains (K≈[〖10〗^3," " 5×〖10〗^4]) that nearly eliminate frequency deviation (nadir as low as -0.0001 pu) at the cost of saturated, impulsive control actions.While these results demonstrate the theoretical capability of CCGTs to provide near perfect frequency regulation, they also highlight a critical practical limitation: unconstrained optimisation leads to unrealistic controllers. Future implementations must enforce a strictly positive lower bound on R to obtain physically realisable CCGT governor responses.
Keywords:
Automatic Generation ControlLinear Quadratic RegulatorCombined Cycle Gas TurbinesCCGTNelder MeadITAE.
1.
Introduction
Automatic Generation Control (AGC) is a fundamental component of modern power systems. Its primary objective is to maintain the system frequency at its nominal value and to keep the tie line power exchanges at scheduled levels by adjusting the generator outputs. With the increasing penetration of renewable energy sources and load uncertainties, the design of robust and optimal AGC strategies has gained renewed importance.
The Linear Quadratic Regulator (LQR) is a well known optimal control technique that minimises a quadratic cost function of states and control inputs. For AGC, the LQR gain is computed from weighting matrices Q (on states) and R (on control). However, the performance of the resulting controller is highly sensitive to the choice of these weights. Traditional methods rely on trial and error or heuristic rules (e.g., Bryson’s rule), which are time consuming and often suboptimal for multi objective requirements such as minimising settling time, overshoot, and control effort simultaneously.
This paper proposes an automated approach to tune the LQR weights using direct optimisation. The optimisation objective combines the Integral of Time weighted Absolute Error (ITAE), the control energy, and a large penalty on the frequency nadir (maximum negative deviation). The Nelder Mead simplex algorithm – a derivative free method – is used to find the optimal weights. The approach is demonstrated on a simple single area AGC model subject to three step load disturbances.
The remainder of the paper is organised as follows. Section 2 describes the AGC system model. Section 3 presents the LQR formulation and the optimisation procedure. Section 4 gives the simulation setup and results, followed by a discussion. Section 5 concludes.
References
1.
P. Kundur, Power System Stability and Control. McGraw-Hill, 1994.
2.
H. Bevrani, Robust Power System Frequency Control, 2nd ed. Springer, 2014.
3.
B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods. Prentice-Hall, 1990.
4.
J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM Journal on Optimization, vol. 9, no. 1, pp. 112–147, 1998.
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